Modal verbs for logical deduction

Solution 1:

While both must and should are "square" modals -- the ones that mean logical Necessary,
which is represented by   ⃤ in formulae -- their usage in English shows differences.

As deontic modals, must means 'obligatory', while should means 'strongly advised'.

• You must include your phone number; otherwise it's incomplete.
• You should include your phone number; we may need to contact you.

But as epistemic modals, should is not just a weak must -- it appears to refer to the variety of cognition involved in drawing the conclusion.

• I see a lot of cars in the parking lot; they must be open.
• It's after 9:30; they should be open.

In the first example above, must is used to express a conclusion from evidence or experience;
while in the second, should is used to express a conclusion from theory or expectation.
You could say epistemic should is a priori and epistemic must is a posteriori.

Solution 2:

Big thanks, that's the essence:

"Must is used to express a conclusion from evidence"

and

"Should is used to express a conclusion from theory"